#### QUESTION

Find the length of diagonal of a square with side 8 cm .

#### SOLUTION

Suppose XYWZ is a square of side 8 cm.

seg XW is a diagonal.

In ∆ XYW,

m∠XYW = 90°

… [Angle of a square]

∴ [l(XW)]² = [l(XY)]² + [l(YW)]²

…[Pythagoras theorem]

= (8)² + (8)²

= 64 + 64

∴ [l(XW)]² = 128

∴ l(XW) = √128

…[Taking square root of both sides]

= √64 × 2

= 8 √2 cm

∴ The length of the diagonal of the square is 8 √2 cm.

Suppose XYWZ is a square of side 8 cm.

seg XW is a diagonal.

In ∆ XYW,

m∠XYW = 90°

… [Angle of a square]

∴ [l(XW)]² = [l(XY)]² + [l(YW)]²

…[Pythagoras theorem]

= (8)² + (8)²

= 64 + 64

∴ [l(XW)]² = 128

∴ l(XW) = √128

…[Taking square root of both sides]

= √64 × 2

= 8 √2 cm

∴ The length of the diagonal of the square is 8 √2 cm.